# An Approximation Method for the Scattering Data of One-Dimensional Soliton Equations under Arbitrary Rapidly-Decreasing Initial Pulses

## TL;DR

This paper introduces a new approximation technique to predict the number of solitons generated by arbitrary initial pulses in one-dimensional soliton equations, avoiding complex integrations.

## Contribution

The method provides a simple way to estimate soliton counts for various equations, demonstrated on the nonlinear Schrödinger equation with accurate results.

## Key findings

- Accurately estimates soliton numbers without solving original equations
- Shows good agreement with numerical simulations
- Applicable to a wide range of one-dimensional soliton equations

## Abstract

We present a novel approximation method that can predict the number of solitons asymptotically appearing under arbitrary rapidly decreasing initial wave packets. The number of solitons can be estimated without integration of the original soliton equations. As an example, we take the one-dimensional nonlinear Schrodinger equation and estimate the behaviors of the scattering amplitude in detail. The results show good agreement compared with those obtained by direct numerical integration. The presented method is applicable to a wide class of one-dimensional soliton equations.